• # question_answer The line $x\cos \alpha +y\sin \alpha =p$ will be a tangent to the conic $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$, if        [Roorkee 1978] A)            ${{p}^{2}}={{a}^{2}}{{\sin }^{2}}\alpha +{{b}^{2}}{{\cos }^{2}}\alpha$ B)            ${{p}^{2}}={{a}^{2}}+{{b}^{2}}$ C)            ${{p}^{2}}={{b}^{2}}{{\sin }^{2}}\alpha +{{a}^{2}}{{\cos }^{2}}\alpha$ D)            None of these

$y=-x\cot \alpha +\frac{p}{\sin \alpha }$is tangent to $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,$ if $\frac{p}{\sin \alpha }=\pm \sqrt{{{b}^{2}}+{{a}^{2}}{{\cot }^{2}}\alpha }$ or ${{p}^{2}}={{b}^{2}}{{\sin }^{2}}\alpha +{{a}^{2}}{{\cos }^{2}}\alpha$.